On the Differential-Difference Sine-Gordon Equation with an Integral Type Source
Bazar Babajanov* Urgench State UNiversity, Faculty of Physics and Mathematics , 14, H. Alimjan , Urgench , UZBEKISTANMičhal Fĕckan** Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava , Mlynská dolina , Bratislava , SLOVAKIAA. K. Babadjanova*** V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences , 81, str. Mirzo Ulughbek , Tashkent , UZBEKISTAN
ABI
Аннотация
ABSTRACT In this work, we study the integration of the differential-difference sine-Gordon equation with an integral type source. We deduce the time performance of the scattering data of the spectral problem which is associated with the discrete sine-Gordon equation. Using the inverse scattering method, we integrate the Cauchy problem for the differential-difference sine-Gordon equation with the integral type source in the class of the rapidly decreasing functions.
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